{
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  "metadata": {
    "colab": {
      "name": "qaoa_cirq.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0WCHbEwRO7R0",
        "colab_type": "text"
      },
      "source": [
        "Overview of \"A Quantum Approximate Optimization Algorithm\" written by Edward Farhi, Jeffrey Goldstone and Sam Gutmann.  "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1jPYX6RNP9Rt",
        "colab_type": "text"
      },
      "source": [
        "# Introduction:\n",
        "\n",
        "Combinatorial optimization problems attempt to optimize an objective function over *n* bits with respect to *m* clauses.  The bits are grouped into a string $z = z_1z_2...z_n$, while clauses are constraints on a subset of the bits, satisfied for some strings, not satisfied for others.  The objective function, then, is defined as \n",
        "\n",
        "\\begin{equation} \\tag{1}\n",
        "C(z) = \\sum_{\\alpha=1}^{m} C_{\\alpha}(z)\n",
        "\\end{equation} \n",
        "\n",
        "where $C_{\\alpha}(z) = 1$ if *z* satisfies clause $\\alpha$, and is 0 otherwise.  Note that $C_{\\alpha}(z)$ typically will only depend on a few of the bits in the string.  \n",
        "\n",
        "Now, the goal of approximate optimization is to find a string *z* for which $C(z)$ is close to the maximum value $C$ takes over all strings.  This paper presents a quantum algorithm, paired with classical pre-processing, for approximate optimization.   \n",
        "\n",
        "A quantum computer with *n* qubits works in a $2^n$ dimensional Hilbert space, with basis vectors denoted by $|z>$ where $z=1,2,3,...2^n$, known as the computational basis.  In this framework, we view $(1)$ as an operator, which is diagonal in the computational basis.  \n",
        "\n",
        "Next, a few more operators must be defined in order to map the approximate optimization problem onto the quantum comptuer.  First, we define a unitary operator $U(C, \\gamma)$, which depends on the objective function $C$ and an angle $\\gamma$\n",
        "\n",
        "\\begin{equation} \\tag{2}\n",
        "U(C,\\gamma) = e^{-i{\\gamma}C} = \\prod_{\\alpha=1}^{m} e^{-i{\\gamma}C_\\alpha}\n",
        "\\end{equation} \n",
        "\n",
        "The second equality in $(2)$ is permitted since all $C_\\alpha$'s commute with another (i.e. they are all diagonal in the same basis).  Note that since $C$ has integer eigenvalues we can restrict the values of $\\gamma$ to lie between $0$ and $2\\pi$.  \n",
        "Next, we define an operator $B$, which is the sum of all single bit-flip operators, represented by the Pauli-x matrix\n",
        "\n",
        "\n",
        "\\begin{equation} \\tag{3}\n",
        "B = \\sum_{j=1}^{n} \\sigma^{x}_j\n",
        "\\end{equation} \n",
        "\n",
        "Then we define another angle-dependent unitary operator as a product of commuting one-bit operators\n",
        "\n",
        "\\begin{equation} \\tag{4}\n",
        "U(B,\\beta) = e^{-i{\\beta}B} = \\prod_{j=1}^{n} e^{-i{\\beta}\\sigma^{x}_j}\n",
        "\\end{equation} \n",
        "\n",
        "where $\\beta$ takes values between $0$ and $\\pi$.  \n",
        "The initial state of the qubits will be set to a uniform superposition over all computational basis states, defined as:\n",
        "\n",
        "\n",
        "\\begin{equation} \\tag{5}\n",
        "|s> = \\frac{1}{2^n} \\sum_{z} |z>\n",
        "\\end{equation} \n",
        "\n",
        "Next, we define an integer $p \\ge 1$ which will set the quality of the approximate optimization; the higher $p$ the better approximation can be attained.  For a given $p$, we define a total of $2p$ angles $\\gamma_1 . . . \\gamma_p \\equiv \\pmb\\gamma$ and $\\beta_1 . . . \\beta_p \\equiv \\pmb\\beta$ which will define an angle-dependent quantum state for the qubits\n",
        "\n",
        "\\begin{equation} \\tag{6}\n",
        "|\\pmb\\gamma, \\pmb\\beta> = U(B,{\\beta}_p)U(C,{\\gamma}_p)...U(B,{\\beta}_1)U(C,{\\gamma}_1)|s>\n",
        "\\end{equation} \n",
        "\n",
        "Notice that there are $p$ $C$-dependent unitaries, each of which require $m$ rotation gates on local sets of qubits.  In the worst case, each $C$-dependent unitary must be run in a different \"moment\" (when referring to a quantum circuit, a moment is essentially one \"clock cycle\" in which a group of operators acting on various qubits can be performed simulatneously), and thus the $C$-unitaries can be implemented with a circuit depth of $\\mathcal{O}(mp)$.  Meanwhile, there are $p$ $B$-dependent unitaries, each of which only involve single qubit-operators and thus can all be applied in one \"moment\".  Therefore, the $B$-unitaries have a circuit depth of $\\mathcal{O}(mp)$.  This means that the final state we seek can be prepared on the quantum computer with a circuit depth of $\\mathcal{O}(mp + p)$.  \n",
        "\n",
        "Next, we define $F_p$ as the expectation value of $C$ in this state:\n",
        "\\begin{equation} \\tag{7}\n",
        "F_p(\\pmb\\gamma, \\pmb\\beta) = <\\pmb\\gamma, \\pmb\\beta|C|\\pmb\\gamma, \\pmb\\beta> \n",
        "\\end{equation} \n",
        "\n",
        "and define the maximum value that $F_p$ takes over all angles as \n",
        "\\begin{equation} \\tag{8}\n",
        "M_p = max_{\\gamma,\\beta}F_p(\\pmb\\gamma, \\pmb\\beta) \n",
        "\\end{equation} \n",
        "\n",
        "\n",
        "\n",
        "Finally, with all these terms defined, we can lay out an algorithm for approximate optimization. \n",
        "1. Pick integer $p$ and determine a set of 2$p$ angles $\\{ \\pmb\\gamma, \\pmb\\beta \\}$ which maximize $F_p$.\n",
        "2. Prepare the state $|\\gamma, \\beta>$ on the quantum computer.\n",
        "3. Measure the qubits in the computational basis to obtain the string $z$ and evaluate $C(z)$\n",
        "4.  Perform step 3 repeatedly with the same angles to obtain a string $z$ such that $C(z)$ is very near or greater than $F_p(\\pmb\\gamma, \\beta)$\n",
        "\n",
        "The main roadblock to this algorithm is to find the optimal set of angles $\\{ \\pmb\\gamma, \\pmb\\beta \\}$.  One method, if $p$ does not grow with $n$, is to use brute force by running the quantum computer with values of $\\{ \\pmb\\gamma, \\pmb\\beta \\}$ chosen on a fine grid on the compact set $[0,2\\pi]^p \\times [0,\\pi]^p$ in order to find the values of angles that produce the maximum $F_p$.  The paper also presents a method using classical pre-processing to determine the optimal angles.  However, as this overview is intended to focus on the quantum computational part of the algorithm, we will assume that optimal angles $\\{ \\pmb\\gamma, \\pmb\\beta \\}$ have been determined in *some* fashion, and illustrate in detail how the quantum computing part of this algorithm works. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mRDXN-03r_En",
        "colab_type": "text"
      },
      "source": [
        "# Example Problem: MaxCut for Graphs with Bounded Degree\n",
        "\n",
        "We will now examine the quantum part of the quantum approximation optimization algorithm (QAOA) using the MaxCut problem for graphs with a bounded degree as an example optimization problem.  The input is a graph with $n$ vertices and an edge set $\\{ \\langle jk \\rangle \\}$ of size $m$.  The $n$ vertices are mapped to $n$ qubits, while the $m$ edges of the edge set represent the $m$ clauses of the combinatorial optimization problem.  The goal is to maximize the objective function defined as \n",
        "\n",
        "\\begin{equation} \\tag{9}\n",
        "C = \\sum_{\\langle jk \\rangle } C_{\\langle jk \\rangle }\n",
        "\\end{equation} \n",
        "  \n",
        "where \n",
        " \n",
        "\\begin{equation} \\tag{9}\n",
        "C_{\\langle jk \\rangle } = \\frac{1}{2}(-\\sigma^z_j \\sigma^z_k + 1)\n",
        "\\end{equation} \n",
        "\n",
        "Each clause $C_{\\langle jk \\rangle }$ is thus equal to 1 when qubits $j$ and $k$ have spins pointing in opposite directions along the *z*-direction, and equal to 0 when the spins are in the same direction.  \n",
        "\n",
        "## MaxCut for Bounded Graph of Degree 2 with 4 Vertices\n",
        "Below, we give the Cirq implementation of a QAOA for the MaxCut problem for a regular graph of degree 2 with $n=4$ vertices and $m=4$ edges given as $\\langle 1,2 \\rangle ,\\langle 2,3 \\rangle ,\\langle 3,4 \\rangle ,\\langle 4,1 \\rangle $.  Note that this graph is just a ring. For simplicity, we choose $p=1$ and arbitrarily choose values of $\\beta_1$ and $\\gamma_1$ (though in a real implementation the optimal angles must be found either by brute force or clever classical pre-processing).\n",
        "  \n",
        "To run, press the play button in the upper left-hand corner of the code boxes below.  The code boxes must be run in sequential order, starting with the code box that imports Cirq and other necessary Python libraries.\n",
        "  \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m8vt0Rw0wrqT",
        "colab_type": "code",
        "outputId": "97f95f50-989b-42e1-fec6-936ae1d3cd75",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 731
        }
      },
      "source": [
        "!pip install git+https://github.com/quantumlib/Cirq\n",
        "import cirq\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import cmath\n",
        "import scipy.linalg"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting git+https://github.com/quantumlib/Cirq\n",
            "  Cloning https://github.com/quantumlib/Cirq to /tmp/pip-req-build-1qjwfhm9\n",
            "  Running command git clone -q https://github.com/quantumlib/Cirq /tmp/pip-req-build-1qjwfhm9\n",
            "Requirement already satisfied (use --upgrade to upgrade): cirq==0.9.0.dev0 from git+https://github.com/quantumlib/Cirq in /usr/local/lib/python3.6/dist-packages\n",
            "Requirement already satisfied: freezegun~=0.3.15 in /usr/local/lib/python3.6/dist-packages (from cirq==0.9.0.dev0) (0.3.15)\n",
            "Requirement already satisfied: google-api-core[grpc]<2.0.0dev,>=1.14.0 in /usr/local/lib/python3.6/dist-packages (from cirq==0.9.0.dev0) (1.16.0)\n",
            "Requirement already satisfied: matplotlib~=3.0 in /usr/local/lib/python3.6/dist-packages (from cirq==0.9.0.dev0) (3.2.1)\n",
            "Requirement already satisfied: networkx~=2.4 in /usr/local/lib/python3.6/dist-packages (from cirq==0.9.0.dev0) (2.4)\n",
            "Requirement already satisfied: numpy~=1.16 in /usr/local/lib/python3.6/dist-packages (from cirq==0.9.0.dev0) (1.18.4)\n",
            "Requirement already satisfied: pandas in /usr/local/lib/python3.6/dist-packages (from cirq==0.9.0.dev0) (1.0.3)\n",
            "Requirement already satisfied: protobuf~=3.11.0 in /usr/local/lib/python3.6/dist-packages (from cirq==0.9.0.dev0) (3.11.3)\n",
            "Requirement already satisfied: requests~=2.18 in /usr/local/lib/python3.6/dist-packages (from cirq==0.9.0.dev0) (2.23.0)\n",
            "Requirement already satisfied: sortedcontainers~=2.0 in /usr/local/lib/python3.6/dist-packages (from cirq==0.9.0.dev0) (2.1.0)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from cirq==0.9.0.dev0) (1.4.1)\n",
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            "Requirement already satisfied: typing_extensions in /usr/local/lib/python3.6/dist-packages (from cirq==0.9.0.dev0) (3.6.6)\n",
            "Requirement already satisfied: dataclasses in /usr/local/lib/python3.6/dist-packages (from cirq==0.9.0.dev0) (0.7)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from freezegun~=0.3.15->cirq==0.9.0.dev0) (1.12.0)\n",
            "Requirement already satisfied: python-dateutil!=2.0,>=1.0 in /usr/local/lib/python3.6/dist-packages (from freezegun~=0.3.15->cirq==0.9.0.dev0) (2.8.1)\n",
            "Requirement already satisfied: setuptools>=34.0.0 in /usr/local/lib/python3.6/dist-packages (from google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq==0.9.0.dev0) (46.1.3)\n",
            "Requirement already satisfied: google-auth<2.0dev,>=0.4.0 in /usr/local/lib/python3.6/dist-packages (from google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq==0.9.0.dev0) (1.7.2)\n",
            "Requirement already satisfied: pytz in /usr/local/lib/python3.6/dist-packages (from google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq==0.9.0.dev0) (2018.9)\n",
            "Requirement already satisfied: googleapis-common-protos<2.0dev,>=1.6.0 in /usr/local/lib/python3.6/dist-packages (from google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq==0.9.0.dev0) (1.51.0)\n",
            "Requirement already satisfied: grpcio<2.0dev,>=1.8.2; extra == \"grpc\" in /usr/local/lib/python3.6/dist-packages (from google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq==0.9.0.dev0) (1.28.1)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib~=3.0->cirq==0.9.0.dev0) (2.4.7)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.6/dist-packages (from matplotlib~=3.0->cirq==0.9.0.dev0) (0.10.0)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib~=3.0->cirq==0.9.0.dev0) (1.2.0)\n",
            "Requirement already satisfied: decorator>=4.3.0 in /usr/local/lib/python3.6/dist-packages (from networkx~=2.4->cirq==0.9.0.dev0) (4.4.2)\n",
            "Requirement already satisfied: chardet<4,>=3.0.2 in /usr/local/lib/python3.6/dist-packages (from requests~=2.18->cirq==0.9.0.dev0) (3.0.4)\n",
            "Requirement already satisfied: urllib3!=1.25.0,!=1.25.1,<1.26,>=1.21.1 in /usr/local/lib/python3.6/dist-packages (from requests~=2.18->cirq==0.9.0.dev0) (1.24.3)\n",
            "Requirement already satisfied: idna<3,>=2.5 in /usr/local/lib/python3.6/dist-packages (from requests~=2.18->cirq==0.9.0.dev0) (2.9)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.6/dist-packages (from requests~=2.18->cirq==0.9.0.dev0) (2020.4.5.1)\n",
            "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.6/dist-packages (from sympy->cirq==0.9.0.dev0) (1.1.0)\n",
            "Requirement already satisfied: rsa<4.1,>=3.1.4 in /usr/local/lib/python3.6/dist-packages (from google-auth<2.0dev,>=0.4.0->google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq==0.9.0.dev0) (4.0)\n",
            "Requirement already satisfied: pyasn1-modules>=0.2.1 in /usr/local/lib/python3.6/dist-packages (from google-auth<2.0dev,>=0.4.0->google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq==0.9.0.dev0) (0.2.8)\n",
            "Requirement already satisfied: cachetools<3.2,>=2.0.0 in /usr/local/lib/python3.6/dist-packages (from google-auth<2.0dev,>=0.4.0->google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq==0.9.0.dev0) (3.1.1)\n",
            "Requirement already satisfied: pyasn1>=0.1.3 in /usr/local/lib/python3.6/dist-packages (from rsa<4.1,>=3.1.4->google-auth<2.0dev,>=0.4.0->google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq==0.9.0.dev0) (0.4.8)\n",
            "Building wheels for collected packages: cirq\n",
            "  Building wheel for cirq (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for cirq: filename=cirq-0.9.0.dev0-cp36-none-any.whl size=1407599 sha256=32feab921e73df656a3323d61449bbf0671f5b88a9bc93ee4975c07b275d1737\n",
            "  Stored in directory: /tmp/pip-ephem-wheel-cache-otlqifme/wheels/c9/f4/ee/029123a49c5e2d75d08c2a9f937e207b88f045901db04632a7\n",
            "Successfully built cirq\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8wn5iclYK49L",
        "colab_type": "code",
        "outputId": "e91f13c1-e3da-4022-e203-83a88361adda",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        }
      },
      "source": [
        "#This code runs the QAOA for the example of MaxCut on a 2-regular graph with \n",
        "#n=4 vertices and m=4 clauses\n",
        "#The graph is a ring\n",
        "\n",
        "\n",
        "# define the length of grid.\n",
        "length = 2\n",
        "nqubits = length**2\n",
        "# define qubits on the grid.\n",
        "#in this case we have 4 qubits on a 2x2 grid\n",
        "qubits = [cirq.GridQubit(i, j) for i in range(length) for j in range(length)]\n",
        "#instantiate a circuit\n",
        "circuit = cirq.Circuit()\n",
        "\n",
        "\n",
        "#apply Hadamard gate to all qubits to define the initial state\n",
        "#here, the initial state is a uniform superposition over all basis states\n",
        "circuit.append(cirq.H(q) for q in qubits)\n",
        "\n",
        "#here, we use p=1\n",
        "#define optimal angles beta and gamma computed by brute force\n",
        "#or through classical pre-processing\n",
        "#beta in [0,pi]\n",
        "#gamma in [0,2*pi]\n",
        "beta = 0.2\n",
        "gamma = 0.4\n",
        "\n",
        "#define operators for creating state |gamma,beta> = U_B*U_C*|s>\n",
        "#define U_C operator = Product_<jk> { e^(-i*gamma*C_jk)} and append to main circuit\n",
        "coeff = -0.5 #coefficient in front of sigma_z operators in the C_jk operator\n",
        "U_C = cirq.Circuit()\n",
        "for i in range(0,nqubits):\n",
        "  U_C.append(cirq.CNOT.on(qubits[i],qubits[(i+1)%nqubits]))\n",
        "  U_C.append(cirq.rz(2.0*coeff*gamma).on(qubits[(i+1)%nqubits]))\n",
        "  U_C.append(cirq.CNOT.on(qubits[i],qubits[(i+1)%nqubits]))\n",
        "circuit.append(U_C)\n",
        "\n",
        "#define U_B operator = Product_j {e^(-i*beta*X_j)} and append to main circuit\n",
        "U_B = cirq.Circuit()\n",
        "for i in range(0,nqubits):\n",
        "  U_B.append(cirq.H(qubits[i]))\n",
        "  U_B.append(cirq.rz(2.0*beta).on(qubits[i]))\n",
        "  U_B.append(cirq.H(qubits[i]))\n",
        "circuit.append(U_B)\n",
        "\n",
        "#add measurement operators for each qubit \n",
        "#measure in the computational basis to get the string z\n",
        "for i in range(0,nqubits):\n",
        "  circuit.append(cirq.measure(qubits[i],key=str(i)))\n",
        "\n",
        "#run circuit in simulator to get the state |beta,gamma> and measure in the\n",
        "#computational basis to get the string z and evaluate C(z)\n",
        "#repeat for 100 runs and save the best z and C(z)\n",
        "#simulator = cirq.google.XmonSimulator()\n",
        "simulator = cirq.Simulator()\n",
        "reps = 100\n",
        "results = simulator.run(circuit, repetitions=reps)\n",
        "\n",
        "#get bit string z from results\n",
        "best_z = [None]*nqubits\n",
        "best_Cz = 0.0\n",
        "all_Czs = []\n",
        "for i in range(0,reps):\n",
        "  z = []\n",
        "  for j in range (0,nqubits):\n",
        "    if (results.measurements[str(j)][i]):\n",
        "      z.append(1)\n",
        "    else:\n",
        "      z.append(-1)\n",
        "\n",
        "  #compute C(z)\n",
        "  Cz = 0.0\n",
        "  for j in range(0,nqubits):\n",
        "    Cz += 0.5*(-1.0*z[j]*z[(j+1)%nqubits] + 1.0)\n",
        "  all_Czs.append(Cz)  \n",
        "    \n",
        "  #store best values for z and C(z)\n",
        "  if (Cz > best_Cz):\n",
        "    best_Cz = Cz\n",
        "    best_z = z\n",
        "    \n",
        "#print best string z and corresponding C(z)\n",
        "print(\"Best z\")\n",
        "print(best_z)\n",
        "print(\"Best objective\")\n",
        "print(best_Cz)\n",
        "\n",
        "plt.plot(all_Czs)\n",
        "plt.xlabel(\"Run\")\n",
        "plt.ylabel(\"C(z) value\")\n",
        "plt.show()\n",
        "\n",
        "#print a diagram of the circuit\n",
        "print(circuit)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Best z\n",
            "[1, -1, 1, -1]\n",
            "Best objective\n",
            "4.0\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ooU6A/Yf74/eD4Wi8yrdtfj01i8DmI8hJFEp83zEw1U4NZUarhPdTjkxVx6c7GGHd6k7ufZY1NVSVRdC3P5+EQ96ycClKDZkLDPN+bvmWibO4YPv2jZablcVTm0XAIQ5GbzvR34ramD4P3cEI0aLGj9/0oIbUa1s5B5MuCFqt2vIIxrJ2kiu9IlFDY90Yvy/WWbXUUIuyr+mUqe8ZNVQw8WkSZEYN2SyCfjV6TbQ/y+rW3i7TUUPhdxzUkCXKyFfuxLOeqY/AQ08WSzVP7sRznKLFU6uPgIgCItoB4DEAtzDzbZbTXk1EdxPRDUS02XGdq4hoOxFt37NnT50iF0J3MMTaVZ3odQFqKEW3pFcBa1d1YIu4mVrU0KTUUH8U68ZYxRXRWRFZQ53ZO48Ki7TdO9yJzcNZXLAC6yTQS5Gk5bD5CPS2ODk1pNqf7bjpyOwOzISyHIvASOBzZdjnyzdDaiha+GXpyed46rqONlo3ap0ImHnIzOcB2ATgQiI6yzjlCwC2MvM5AG4BcJ3jOtcy8zZm3rZ+/fo6RS6Ebn+EIxdDdq0QNdRx0y2qca9dFV7XjLhJ5BEEdUYN2ayXYlFD6jeY5rLt+ESy9lUnazvlU3q0y+TrI5gONWSWIvGRIxxA/NuiC/EA17bSHPZ2aVA9uT6C9CTnG4gQD6juZz0NJOXQKaB8/eUllI2f4xSpr6lEDTHzXgC3ArjEOP4EM3ejtx8CcME05KkK3cEIqzqtaDVTkhoyNjtRD/8oY1WgVrQLU/YR6PdbKLBDV3cwSv2GrOMTyRrp9aiM1ZY6fpTNShkME7/ThXaLQFOgJFQpElcRPLuzuBq96nrKbJcZ+lsI8qkh87f5Wpuq/R21qjNjH4FDT47jS5r+skqFJ59jA6ghIlpPROui16sB/CyAB41zNmhvLwPwQF3y1IFw1RZYs4Pt5/tTQ0etTq4KVKKPWXSu/qihkrWGBqP4N5gD1vi3VessPmp123nN8UBmk8mz1lBYgbX+XcpslqMOex7BEEcutsOJagK9JnVpGeAM/Q1HjP6QCyaUpUNjfQMREvLNNGpoiKBFOGLRtOj99GcrFa4c8rY2WjfqjBraAOA6IgoQTjj/l5lvIqL3AtjOzDcC+HUiugzAAMCTAN5QozyVQzVoX8rEtiG5+V19dau/j62JafkIlLM4GQ0yMCJubFCRT/HqMWkiV28R2FdhyXPselXf90koA9SAVe8AFLeTIj6CkBqadKJKWldhqXAicuqvZ13c2PfiHt/DMvEWpYaynvU0oH7DYjvAod4gPm7oz3ZcvV+9kHy+Kat1ihNdbRMBM98N4HmW4+/SXr8DwDvqkqFuxI2hWCM28wh6kVM47HBq5ZAcLG3frbPWkNUiUFtr5kwErt8AhDqzHZ9IVkUXrO44JyqXTCrRx8ciAIpZRWVh031SBjs1dHw7KOTHsd67H+tJlQrvBFnt0h4Jp18rdY/BEGsWkkOPv7M4ftaz9hGovv/UIQuFttpBGWW0/dQ5TfMRNBVjashzU3N1js6Pmma0i4u1DQ7TzyPwC/NLr2ySHeKIhQBBK15lTiyrcT9bRqZLr+Pieh6Zxeq8ZUkNRdm9RbK/s+5tPrvcdmnNLM6ghkyLoONrVcdyZBW2qxuuvl/Gx6JfM3FOU6KGmo54VeDLb6Y3JDdXd/GKJxndYqMLwv0I6mksNipKvc5Lfe+NVzb2qKHFjr9fxQfm/Wz8q5I5rdc0tZGFxXYw8VaQebDRLUkZLNSQsk4LFAa039tof8ZuWz76U3SiS089q4+gNb53pnzGc5xmGYaEHAla2B4dpE9Upv56w/Rv9WnHdUEmggmg4s+9qSEHNwqkOdfx6nZgrFynVmtolNiQPCFrrkWQXNmo36CcYTGdVr2PQH+fOKdvl6k7TFMbWZh0xe0DG92iox20ELTIGsI5MTXksK7c7TKDGnJGDaV9Mv5RQ+E5thyVaUKnhvQBuzcYoRMQ1iwkF02m/mwbWc3SRyATwQToFhzUXPHTQNrUTnGxljpFYR5BTfsRDJIbkuv3zmugrt+g79BmrqQmgRnjbje7c/S6LH0EbislnZE+LOSvyru3qUuX/pYs+mu3KDOD1pYjUcSq1gfaWfkJ4ok3TQ2p40C+/hLX7OefUxdkIpgA487ny2/aOkDHQQ0ZyUG2waFuiyC9avPrfHqCl/5e/w1Vcu3dwQgLQWschWEbCOPVlkFtjDnuIlFDNU8Elkk/LUcypyOOYJs8aqjdIhyxaG9/PvoLw2zdfcLuI/APuEgMtDMKIU30fSOnQh1X8ur/Tf2Z10yeIxPBioCqw26rIGo939YBjAadXjmY4aPpqCG9DEVVsK/afC2C8PM1C0EUcWL4OdSAVVWtIS2UL7x/hiPOI+olC0XqLZWFj0z6QBtTbsHEE5UeCafLUlR/oa8iI3zUmlnsv5iaZiVYqxz9UcI5r/pgUf0lrhkdqyIfpChkIpgA+irMx7HT7Y9SGawL4waTE51hccq1o+pUdRgFtnr4RaOGTM5aj3yqmhpSz0G9T51TIBorC8uFGtLDLRN6nXCiUvRlKoihoP5cenKVz/DPxTEG2pn6CMJFoAqzHR/P0J8PfRn7HcUiWPbQ48+9G3EUcqYjzSWa0RlGhzN2KANQS70hKzXU8aSGtFWizlknJ4hqqSEbL2ueA1QTNVT/ROBjEdj0Wg01pCYUwMZx++nPpSfdT5T6Pb5WdSeY6v7RdjnslonuqwGS+ltot7Cqk0Ff9vV+U3870yETQUnEUTxBQX4zvRIKP4s7dYuAIxZMLjY9OCiLoA4/wUTUkMZx6xRQYoKo2Edg42WT54T3PmKhnXBkxhnUBSyC2jOLPXwEHYteO9VEDWVRG2ZlTJf+XE5rl7Xjn4uzTKihcZtTA/7QflzTX1Kv7sXKqgryQYpCJoKS0KNNfPluRSXpMBuGWt2ucjibzDwCALVEDmX7MwpQQ5ojPTlBVEgN9cOiZ5nU0LiTuekqH0w1oSwzasii13FbnIAa6se+Bl2WsUPe2S5tPgJbZIxr4gh/T56/yzVRTRu6f1DJlTye1pPteOKaZjCFZBYvf+groUmooVWpzOKQ7x77DvrxccBhEdSwOY1q0Dp86/F7U0OVbUwT53Po90mco1VT1R2ZPoOujmVPDU04Ubn8LYqb7wSUcGQ6V/gOPWX5FID8BLHxQDvF/aOtcoz1ZKGGMvRnWhDmNQGhhlYUzEGtNxxhlLMytyeUqcE1aVoGLUpG3Nh8BFGGcj0WQXpDd/+oITtnnZ4gqpoIjJA9R/q+2ic3IZNlgs3CNEx2n9wGu14rpIZSPoKwPZgVWN0r/ILUkLe1aR+Apw03hZatP5/FSuxDE2po2cPkuwGP0guW4mYuaij8LE1h6HWK6vURTEANjSmgZDhjsqFXV6rBhy7I06u/jyDIrCdfBbqDEQKjFIlNDlu9H98Itqx7Z1Eb43vnUUOOid4dbuprbS4Tamhgt0zy9LcQZEwExnMUi2AFYCnBy/onWuUlaelO2qT5n65TNPWoId/fmXIKp62aKuPxXXytKZNdrwWpITXp19hJbY56mxzpyJ2wLfpYp3n3dq101X1M/aU3mrHnM7gc4UWszbxnXTdUmXWvqCFDf7FF5aaGFgL/+mVVQSaCkogHNf8sRyvdYkYXaPH7iYgbC61Uq0Vg2dDd5Ied340in9omDVMnNZRDF+j6s0bcFKCG9O/VAZs1ZpPDSg15WqfOe2uJUup9+D/ehczUnxrgEvI5JvpKqKEcGrBumCt3JZeSx0YB6f3J5R9TDvlWi6aSuKhDJoKSMAc1wN+s1TE2FQ3TEkAy4maQzsasPWrImLR8d+hSv8EsNZD0q1TnDFN6zZqodP25Im58MA1u2mY52uSw0TO+bdF57+jZqcJ2tvZn6s+mu8LUUNuTGkoNtNOnhsx2rORSn6loudTxTrpfJ67bN62uBlgERLSKiL5JRN8iovuI6D2WcxaJ6Hoi2klEtxHR1rrkqRrJSA1fyiTdwVstwkKQXN25qKG0RRC+r89HkB6MfAZwFfkUnq9TGMnJs6p68smJxz0AuaiNBcuK1oVJB1of2CxHmxxm5M6qhFVUboD0aX+m/mx1mpxRQ64EtAIFDRfbQW5huzph8w/6UkPqey5qKO43zYka6gK4mJnPBXAegEuI6CLjnDcBeIqZTwPwPgB/VKM8lcL08APZjVjnFU2kOpZlVWCzJsYWQR3how6e2ieaIfEbEjRC0kegH5tI1oTZ7Q5btOs1n4/XMY2MVi9qSAsT1feqmJQ792l/PvrTJyrz+kp+83wfuXUqatqD5VgGI2FSyRWWzwj1ZE5U6YnU1UaD+Jwm1BriEAejt53ozxyxLgdwXfT6BgAvId+l2YyRzCPIb8RZ0SnJTm1EZ/TTxxXq8hHEG5JbVnoeiS4+kU9VUiw6jeVcbbn06rB8XJgKNeQh02I73j86aZ1ONlHpBeFc7S+tv+w2nfxtOdRQhl71gXZ8jykOlgpWamgwQn/IYA6pnxQt6tCfed3Eb2uIRQAiCohoB4DHANzCzLcZp2wE8AgAMPMAwD4Ax1mucxURbSei7Xv27KlTZG8kedl8fjMrOkUPpUyYhx3DNDcmkSCoJ2qolzVp+VBDHpFPVXG88eCg+FeXI86hVwfH7cJ0nMUeUUPt2CncswxMto1P8mAWhHO1v7T+7G16YKH+cp3FGQO7PtCq78ycGtLkNic5M3HRpr/EdXWHfIOoITDzkJnPA7AJwIVEdFbJ61zLzNuYedv69eurFbIkxqvbtpYFnDE4ZEWnuEzwpO9gelFD+bLm1xpSOlFVMpk5cbyqzFBz5zZdZwmZoogM8xwfPl7HVHwElsqvWXLo1qZZzbYIVEE4u55GWCygP32iSv42e9syM+xt0MMrAf8N76uGve+PEseVnLqebHo1r7uY6DcNoIZ0MPNeALcCuMT4aDeAzQBARG0ARwN4YhoyTYqivGxWIbEFw/GXWN0mJoLpRA1lWy++UUOxRcAcruaSx6uhWHTLTF3XmVCWWJGVpIY8AwMmgRc1pMmRjD8vb7GY9GVKT+PjRjSbY8EApCdMt48gX68p+RzPum7Y/YOjdFv00F/iuloJmsV2q/bERR11Rg2tJ6J10evVAH4WwIPGaTcCeH30+goAX+U6dlmpAfpD91vNZAyuicJspuMzNs3NvQzqihrS6/KYWHDEQCe+n2jQcRSL2dDV8SpkzeNWTZn0idf2O12IM0PrpYbMBC0Tuv6UtdOK8jbC48UnKn1xo/7rEV82R2aov3SbXnAM7LqfKHm+j1VtTvrTLcwWyxFbNXGY7dCpP33joFjunMVKdO60NrCv0yLYAOBWIrobwO0IfQQ3EdF7ieiy6JwPAziOiHYC+C0Ab69Rnkph9xFMQg1ZuEStodu47PosgixZ81dh5upbHbM19MktArPzuapeOqJeLIlzWagy2skFXU9OOTT9JX9b+USrrIHWGTXk0J9rou8OhtbyGT6UW3qgnS01ZPZTl/5sx20DvNlGw3tNx+Jp13VhZr4bwPMsx9+lvV4C8At1yVAn1Apdxa6Hx8o6i1s42B1gMBxhMGJrQ7eZ4MHYR1BtZzAbrilrLjVkbdDGgFWRj8BGF+w91LOepw+WesSN2jXKB1PzEXg6i8OBZmiZeCughtotHFgapKN1NEdmLyNqSL9m3m8rRA3l0IB1w7r4GIzsE4SNMnKGOGtW1xQWHDqm4iNoIqyrsJI+AhVOZjo+Q8pIT+ixh49WnUcQh8Zm01hZ309RQ/0pUUPOGO2hltkZOzLLh4/WHTWU5yNIUkNpvZaxCOzUxrhdavpL5r3Yo4YAu4/ANhEUooYsPoxpIt3mgkxqyOxPWeU3qrDsykAmgpIwnbrhsZLUUNQwXIPaeEVmho/WFTWUUXbBJ9HFpBHUsXqcxUbns0xU6RWtfTXtg6lRQ7kWge4srkavLn+LjdpQjsy8qCEbNWSbOOKy6wWpoVnWGsrTkzpu69euPIKO2W+mY/HIRFASukls1guywScSJ17xxA19HHGTVXSuYv96HjWUW27by0dQTUPvWQYpk38djKL4c8tgWT6PoL4BqGeZ9N1yDFMF4YBsf5XzvsNkGx1z3JYVsJIzq4nloN4AACAASURBVNaQOsf3t+n5NNnyxXKULa43CXqWfpr0BbiOaxaERW7ToQwINbTsoa+EzHpBrvMB1+AarmLTg1rU4YajaC8De/hofXkEjhoyBTOLgbCRJxp6bT6CtNlt66BjmSx6zUJWPfkqYPqJXNDLYYcTbAXUUN/UZTBue+q9fo/eYISuQ3+uMNssa8f27KzyzagMw1gOM3FM6cnirzIT/tT3eoP0tpzJZL76w5R1yERQEiY36t2IHWZ0MjMxOVge6g6sdYpU+Gj1PoIMWT14WTOzWB1LHq86j8Cdvm/uopXg1wtGDWXVk68C5qrXhSQ1FP+GSSaq9AAXtUuH/pYGQ7ez2EkNuSfePKpn2fgIBnGZdSDu+079DVztL5bdSV8KNbS8Ya5s8hpldh6Bm4sFgP1L/fF5OlSJieotgnxqyLXxiVmnSHd61dHQrWn9llVo4hyTXy/gI1DXqYub9i2LnfRzxHqdZKJKTarOdhl+fsDRLhPypZ6Fe+LNC0SwrcRnNREstoNxxVpV1qSo/nTZbeUzzHPqhEwEJWGuJPMoEx9qaMlceUUNZt/hQeK9QnsmmcUxXWVDyjzWfQR9Cwc6KTVkoQvMicpFDS31kxE3vvCJnCoL00/klCHhI7BYp6XyCNID7WDEONRLtj/1uatd6vKnrbMsH0GOVW3j4GeSWZx0kKv+a5bPGB93tD9ddpvuw3vJRLCsofOyQBF+0716OtC1d7ixRWB8t7Y8AseG5LoMrgZqM4/Vcd2vYm58UlpWCy8LJCcql0yxvktYBDUNQFkLhoQMRomJxMBUcqJK+whU+0vqKa9d6scKU0NeUUPxs55mGYaxHCYbMKaG7P6qtNzpPmSLOAqPCzW0rGE2hrwCWN2Be0Pyccc6nOxYqjGMjxsDc/0Wgd1HEJ5jb6A2zl4dd3WgyWT16GTmABcNoqa+fZE3YE2CLGvMlEGdX5VeXStXs/356K8UNZRrVdutzWmVYdDlSPsHtaJzQXKiOhxNBKsM/em6cVsNYhEsa5gN2offzOJGAW3lZaxu4xXZtKKGkg06IWuOk9cWMx0eT9MwVQyoNl42PD50n2OudHNoGBM+kVNl4esjGG98UqFe0/4We/vz0Z+rnWRGDTkSrfTvAvpAO91VcyyHnRbuDuIy64C2kHPoL9FGHbSwTATLHHZeNrsRZ4XNAfEKy2zorpXXOGqohvDRxbZ9+8a8zueKkHi6N0xFPvkUsMuV1SiQZ+tALquhtEWQM2BNAlN/LugbnxT1Vznv7ZjEU5aqh/5c+0dn7cecSw2ZA+2UB8uxHIafQ08INS0zwK0/u0VgUENTCo+ViaAkzGiTfH4zuwMAenRQklaJudgpWQQZSVaxo9XlI0iuvtWkZot8qqJWTHcwRCegsS7sqy3TajD1uvKoIUANQBZqqOREZdKXrvaXPp7Wn2v/6KxM7rwoINdAO+3s4ixqKOk3zNaf3Ucg1NCKgtU8zKOGMjoAAOw/bDjlxj6CJGWkUF+tIfuG5KEMOdSQsfpuB+H+rfstESZVUUPmNYHkRGVz4gGwyuSDOsMWfZ3F6pw48sl/UZJ1b/uK1qAszXbpXOCk9TRRQpk50E7ZoRrLYe/7RfVnpYai79SduGhCJoKSSA1AHvxmFjcKpFdYedEZrVZofldffTTLoZdDDVk47sV2y/obqkgIsvlqwuMe1FBGHHwW8mjASZCVeJiWI4gjn4yVaLmJIG1ZAB7tskA4aGbUUCcvoSw9AKtrThO2iXc4YjzdM9tiUk9p34Z7sVJ34qIJmQhKIN5owliF5UQ85FJDhx0m+GE7NQSEVkEdUUP5E0EONZRYuQXWyKdKqCEXXZDpLJ4waqiTXRNnEhSihtot628oO1Gl/V729uerP3NgHwxH1gx5/X55kXd5z3oaSOlJi+5z6U9tHKQfz4oaCl9Pr6hebRMBEW0moluJ6H4iuo+I3mY550VEtI+IdkR/76pLniphzt6AHzXk2glLj8IgCh1t5nH9vY6gRTX5CNzmvjrH+l0LtRFaBA5qqIJaQ2Y+hzo+Pscwu5Uj0xWNlYd6fQT+1NBCQq9Jq6jMRJXKRzDan1nYLk9/Zp+w9Zvk+fm5ODYacPo+gnRCGRDqw6U/u2/DnVAGoNbERRO1bUwDYADgt5n5TiJaC+AOIrqFme83zvt7Zn5ljXJUDufsnduIs30EBw73oUfrqEZ1wJFHAISRQ7VEDbk6q3ceQbLhH3CsXA9Eg8lEstroggwfgTK7bTL5oE6TPSuHwybH3kNpa7G8j8BODR043Lc65PP0Z+opz9pRcjOzNWLNljinX3dacFkmBw73cdyRC9bjZpSRus74mv3iY0qVqM0iYOZHmfnO6PUBAA8A2FjX/aYJ++ydn1CWR7fsX0qalqmIG0sHqsUimIQaGnPcSRPZ9huqiRqyD162AUjPi9BlWlXYRzCFPAKP3IaEXlMRbOWihqzURl67zFzhu301qfM7wbjsulu+ZUANWfyDQFpPenSaTa951lKdlqeJqfgIiGgrwm0rb7N8/Hwi+hYRfZGInuv4/lVEtJ2Itu/Zs6dGSf1gd4gG1tKy4+84NuRQ3wXC6AL9mumIG5tFQBjUsFVlLjXkGTUEhI3bFvlUibPYRRcYA1DbyOoO+fWS1FCNVS8LRQ3pejWjWErWGnJFvejHlUXlFTWUkeGdPj/f2sx71tOALW8DSOvJpT+7H8tGqda34DBR+0RAREcC+DSA32Dm/cbHdwI4mZnPBfDnAD5nuwYzX8vM25h52/r16+sV2ANWh6iHEzWPbukN0+cstluZpYnr8RFkZUGn+c3Edx3UkO03VOMjsPO1ptlt/p7FTrZes6B+j6sC6yToDpIljn3kCF+bEWzlEspsHHe4Z0OxdhnLUYwa0s9LyeeKEJtFHoFLT47jC7aJICOPAEjrr0549QAiWkNEv09E/zt6fzoR5fL6RNRBOAl8nJk/Y37OzPuZ+WD0+mYAHSI6vtAvmAFcDtHwMzdlkke3hK+TnUQ1dledonaLKs8j6GXlEfhGDVlMYdvr2qihfnIAMn+PSyYfqPPr2B1LrXptHLlLjvB1euItOlGlKQ/769RnmT6CAtSQR/kS20A7TWrItnGQ87VDf0SUqk1mZsiH11p+1NBHAXQBPD96vxvAf8r6AoUt+cMAHmDmP3Wcc1J0HojowkieJzxlmhnGnHMBvjJrJyxXhwbSsccmgmC6PoK8RBc1AKvIJyCpp6obeneQXG3Z5OsOhqm6SQl/QYk8AqCelahZ4thHDiD5Gxa0lWihext6cr3W3y+07aVIQvkcUUMZeQRAtrWZkGkG1JDSqatNu3S2aOhvMTCtpZC+DFp6v1l+UUOnMvNriOhKAGDmQ5S/ZHkBgF8BcA8R7YiOvRPAlugaHwRwBYBfI6IBgMMAXssukn0ZweUjANyVELPoFtuEMn7faaXO0VFX1JDrfvFqJovHTQ4ONssJiOiZShLK8nwEFsqt4x7k8rCQmPQ7RUXOhDnYZcFGiemvu4MRVhUoqGfqSYXZhhum2PVnDnA6wlpS6VIfrraVu8jweNZ1w5UwOX5tiQ4yX6v3qTZqod+mVWvIdyLoEdFqAAwARHQqQgvBCWb+OoDMyYKZPwDgA54yLBvEJq4t3b24jyBoEToBJXb2Gl+3nWMR1JZH4O7gWdy+q0HbX4cbnwyGIyvtVUZW20Rl9RFE7zsBjRN9fFHnAJTVTtJyuKmh8FrFJiqbLhfbLSxZ9afqNuW0k0JRQ8X60HjimOK+xS4uf/za2dbT+kv6CIYW+nLyhZIvfHvfuwF8CcBmIvo4gK8AuLo2qZY5XA5RwE4X+GxI7upYZjaniWlHDSlZMldtWXy8hVuehGt3r6SMTpaaYLP1moU4fr36ASgruiwlh8O3VJa6KqKneIHi307yE8qU89ddvsQ2UU3VInBE99hem+HKOlI5Fo7JdllRQ8x8CxHdCeAihKv8tzHz47VKtoyhHs4qi2luGxx8olMW2y0c7NpWDtO1CEYjtkaJmDJl1Rpy0Vvqu+brbn+ENQsoBdfE42N2m/L4Qn3HVYF1EuRZY0k5HKvSkolWRfTko7901FDakrZd0yZ3uLm7baKa9kRgj/e3vdYnqpTvL2Ut2fvNtBzhXhMBEb0wenkg+n8mEYGZv1aPWMsbcckCP77SZ7MR1wrLrFhooupaQ+NJK8vkzwhPzBpMzLDISTNDw8HBYREYYYtm0pi5SXgR1E4N+U4EeRNswUEky5eSPh7qz8X3Kzn6Q8ZoxGi1KLcfZEUNDUaMEVsmpM7kkWdF4MoAjuWxtUWbXs3FimOSm1JorK+P4He016sAXAjgDgAXVy7RCoA1Jj6D37TlHZhwDUx5FEbVFoGtoZtQyXPW71toJf032JzIZTvyYMShI9OyktLl6w1GOHp1kisfT7wFdycLv5sdGDAJejm0XFKOHGqogHxxQbiC1FBWm9bCbFe1Aq+8A8Cu155lJa6uNd2oIXtNoFgeS5jt0sCqv57W7nu2yaIdoFtDiLINvtTQq/T3RLQZwPtrkWgFwL4qcPObPtmicccqZoK3W61K8wh8Zc32ETh+g8P/UbYju8IR09RQOmJrImqoxjr43cEQxxzhx5Ml+GjLpFBkNekapCeihjTqb1Undo7m56jY+pDrWU+ZGsqLGiqgv4PduM6Wy7JV1Qp88komQblQDWAXgOdUKchKQhZPmGkRZK6yHdTQlH0EPkXPssLaXFyn7ZplnZrjexn7vCbky/URNIAa0iKfggTlVnyictE27oEsX3+mHJMklLm+O80yDKEc6clM7R8dHvfXn5lZ7KKFpzHR+foI/hxR6CjCyeM8hOUh5hKqUdqiAsr7CMpRQ+2AKl2ZxnvmZtNYqhZ9+vsjrEvRMA56YcKVtWvSMicqW1nteHIqTw3VNxF4UkOO31BmonLRl3E0W3H9mXrKK58RLwwsFoGjTtE0HaqAfUJS+0cf7mdEXVn0ZzrSXf2maD5IGfj6CLZrrwcAPsHM36hBnhUBlfTT8lyF+WxI7uzUOc7imVkEWYlzaxdT59uuWRs1ZExURegqH2QNWJMiK/EwLUf24qHYROBYcedYc3l5BPq188pnePnZZk0NuRYfnVY0EfjrL1UPy9FG60hcNOHrI7iuVilWGLISlGxmaiFqqLCPoNqoIf+JwFFKY2Cp6+OKPJnQWeymC2qmhmo02YsllOVRbgWooYyB1n4PD2oo+kyF2eaVz8jKLM6ihvY6rNM64PJzFKV27SHODstuCtRX5kRARPcgpoQSHwFgZj6nFqmWOewrzOL8pu37KyVqqFhmcQ41VNpHkBVJYhSdK5EQ5cKyoYYckTtlJiq3j2CChDIjPDjP/6HKrhd2Fk81s9g9IQG2tujWn7lDmS00Nvxs9j6CFbVz2LRg66wLGatbnw3JyzqLq6415EtjZdeDKeZwrCVqKNK5a59cl8nug0ktmSzY9OeUIyfkuBQ15Bvx5aE/FzWUhXCAzPCzWeLxp1WGAcj2S2UeL1lrKPys/okucyJg5u/VLsEKhO2hqXpBpaOGXFzisvURZGUWu2LRp0QNaZ3MVdbAtYLzQV0m+3DE1npTeXJUoVe3vyWHGvLyEahnkT/Jufbp9aUB60a+nix5BHBTQyo0NPQRTO70LwuvXkBEFxHR7UR0kIh6RDQkInOTmblBt2+vzumiTApRQzOuNeTnz8iqNZSRnVpBdEviXg4aS5+o8rnv4tSQrZ58FXAlTbmQZ0UWmahyKY8y1JCRz2BziKa/Y19kZDuLp5lZPARRssy6LpfbUrDrrzccaeUzHJbdFHwEvsuhDwC4EsB3AKwG8GYA19Ql1HJH1+IQBXwacfXUUNAiDKtMKOv7TFot67acrjpFbvN4soaetdrXV6G6DCmZSlBD6ntVD0BFtqkEtNWm8fvLTFRZ/habTD76S+cReFJDyzyPYLGd3oOhaLCHvghyl8+YHjXk3QuYeSeAgJmHzPxRAJfUJ9byhsvEdTZijw3JnQ0mh4ttBzVFDXmEupq/1bZtov5+atSQNlFlccu27/oiyyoqCx9rLCmDu20Unaiy/C1AOf2VooZcVnVmHsG0JwL7IjD8X0x/3f4o12pdDs5ihUNEtABgBxH9MYBHMaWN75cjuoMRjlxMq64ov2l+13aOKyFFoT4fgV+ikJ7okp+dmrymysisPo8g7kC51FDJRB2XU3MS+CQemjKE/20DU7GJKj+PoLj+bAlltn5j3q8oNaS25Sy6r0QZuBeBjv6bS4sOM7KSpxc15DuY/0p07lsBPA1gM4BXZ32BiDYT0a1EdD8R3UdEb7OcQ0T0Z0S0k4juJqLzi/6AWcDmEAXU4GBvxHkbkjtDAWcVNVQgGiT1Xc8IE5WRWd5HkM1rhxNBTdRQDRmtPhFbCRkyYvmLTlSlo2F8qKHoObn6TUrugtQQUM/+0Ta4/By5iXcZ1FCe7qcRHutrEVwA4G+YeT+A93h+ZwDgt5n5TiJaC+AOIrqFme/XzrkUwOnR348D+Ivo/7KGLY8AyGrE+RuSuxvMrPIIPCYCY6ApSi+oY2UbuttHEE9UuTKtYGpIbSXp1GuZWkOuEhMl9GelhnKdxWGpBqd8zsGy/jIMQDY1FLQotdNenv66/RFa0biQZdnWDd+J4FUA3kdEXwNwPYAvMfMg6wvM/ChCCgnMfICIHgCwEYA+EVwO4GPRPsX/RETriGhD9N1Kccf3nsSH/v67lVzrB3uXcO7mdanji+0A9+7eh1/76zsSx+9/dL9XBwj/F/QRWKKG/tf/ewg7Htmb/SMAvPiME/CL2zYnjnUHo8wNyUOZQlnf+dl7Eqa+qqboSw2pz77y4GN47MAdqc/ysPOxgwDSew6r+119w9041M2zUspTQ3d9f2/qWU+Cpw71xtf2gdr4xEUN3f7wk97yPbTnoPXebkd/vv7Uc/nsXbtx7+59+OH+JVyY6yNo4e5dab1++0cH7ANtJMdv/t8dKdnXLLTxrleeiaPXxOUZmBnvvel+/HDfUqYcLtzxvaew3iihEsodOC0zXU5T7j+46X60A0qcq18TAD5+2/fxjZ3hPmAvfe6J+LnnbSolexZ8S0y8kYg6CFfwVwK4Jlrdv9nn+0S0FcDzANxmfLQRwCPa+13RscREQERXAbgKALZs2eJzyxQOdofjxj4pthy7Bj/9rPWp4z975onYe0cvdZ/FdgsvP3tD5jW3bT0GLz3zRDxj3erE8WeduBYvfvZ6nLPpaOv3bBbBNbfuRKtFOMHSYBV+sHcJ3338actEMMzckBwAzt54NM7ZdDR+tH8JPzI+O2fT0ThrY1LWNQsBfv55G/ETpx6XutalZ23APzz0eKlnQwS84uwNqcHh3M3rcPbGo/GDvYcBAOdvWYdT1x+ZOGfjutV46Zkn4oKtxxS+LxA+68/v2F1Zm1I4b/M6PPuktd7nv2bbZmtbfNlzT8TN9zxaSL5LzzopRV9u23oMfuY5J2LLsWsSx08/4UhcfMYJOM+yIFIgIlx27jPw4A/346E9B3HysUfgp05Py6rj4uecgEeeOpSSO2gRXnlOug89b/MxOGvjUdj11KHE8cP9IR558jBede4GvOjZJ4yP7znQxUe/8TBOWLuIdWuK1+9Zt6aDl555Uur4i89Yn6gAq3DRM4/DK87egOOM0uJnnLQW521ehyeeDrd+P3fT0TjzGUclzlm72MZLzkjq44mD5dprLpjZ+w9h5aNXAfgMgMc9v3Mkwk1sft7y2U0AflJ7/xUA27Kud8EFF7Agxp98+UHe+vabEsee9Xs38x/efH/m9976f+7kF/+3W1PH3/GZu/mCP7ilShEFgqnjnl17+eTfvYm/fO+jiePff+JpPvl3b+JPbX9kRpLNDgC2s2Nc9bJBiehSIvpLhHkErwbwIQDpaTH9vQ6ATwP4ODN/xnLKboSOZ4VN0TGBJ4JWC8xhDD+gb99Y0ilXYM9cgWC5YpWDXy+aqzEv8NXG6wB8DsCzmfkNzHwz5/gIKCSZPwzgAWb+U8dpNwJ4XRQ9dBGAfVyDf6DJUPyiihzK2w5QwZ38lu/QEwiWO1yhl0sFQ3TnBb4+gitLXPsFCMNO7yGiHdGxdwLYEl3zgwBuBvByADsBHALwxhL3mWsoXlL5CXyymMPPXeUw/KtfCgTLFe4Q5/zkznmEb9RQYTDz1xGWq846hwG8pS4Z5gHKuRdGDuXvC6vgyshUUUMCwUqGq06PUEN2iDZWONIWgV9D1zMydRTZIUsgWK5wxeD7WszzBtHGCkdsERSnhoB0Rmbe5iECwUpAvNuZQQ15bLw0j8jt8UT0fCK6JioBsYeIvk9ENxPRW4jIHtwumBpapkXg2dCzsoOlkwhWOlotwkKQpj+LlvGYF2Rqg4i+iLDk9JcRVhvdAOBMAP8BwCoAnyeiy+oWUuBG2iLwa+iuErcSNSRoCmz1loQasiPPWfwrzPy4cewggDujvz8houNrkUzghaAVNmi1J8G4oedkB7s2Cpc8AkFTYKu3VLSe07wgs8erSYCIfp+IErUIorIPsEwUgikiGTXkt59A+LmKs053FOkkgibAVhhwXLFWrN4EfLXx7wB8iYherB37tzXIIygIFTU0YuUjUFFDfj6CJUt4nVgEgibAlj0v1JAdvtrYjbDg3H8lot+JjtW/C4QgF+WjhtzhdbJaEjQBC5b9QVR7NyvWzju8tcHM3wfw0wDOJKJPIdy7WDBjKItgEPkIep4c6Dh8VJsImBk9oYYEDYHKldHRHQxzy6zPI3wngu0AwMxLzPxGAH8HYCHzG4KpQNUaSpWYKBE15FunSCBYCbCVUZFgCDu8NMLMv2q8v4aZn1mPSIIiUFFDqfDREtSQ8KeCJsEVNSQWbxp5eQRfIKJXReWkzc+eSUTvJaJ/U594gjy0nUXn/KihxETgWadIIFgJsDuLJRjChrw8gl8F8FsA3k9ETwLYgzCR7BSEFUM/wMyfr1dEQRYCM3w0GszzCsfZNsaWglyCJsEaPirBEFZkTgTM/EMAVwO4OtpucgOAwwC+zcyHMr4qmBLSFsEQnYCs2+bpsBXlEmpI0CTY9twIfQRi8ZrInAiI6DQAJzLzN5j5YQAPR8dfQEQ/ZOaH6hdRkIXAEj7q09AzqSHpKIIGYLFjKzEh1JANeRp5P4D9luP7o88EM0Y7VWLCr6HbNu6QglyCJsFJDclEkEKeRk5k5nvMg9GxrVlfJKKPENFjRHSv4/MXEdE+ItoR/b3LW2rBGCmLwDM8zlZ9VKghQZNgo4Z6g5EEQ1iQ5yxel/FZXkLZXwL4AICPZZzz98z8ypzrCDJgyyPwaehEFGZeWn0E0lEEKx8qaoiZxwlkYhHYkaeR7UT0q+ZBInozgDuyvsjMXwPw5ASyCTyQihoqwIGaK6a4TpF0FMHKx2InADPQH8a78ImPwI48i+A3AHyWiH4J8cC/DWFW8c9VcP/nE9G3APwAwL9n5vtsJ0WVTq8CgC1btlRw2+bAlkfgPxEEVotglfgIBA2A7gdb0KhQsXjTyAsf/RGAn4iqjp4VHf4bZv5qBfe+E8DJzHyQiF4O4HMATnfIcS2AawFg27ZtbDtnXmH3Efg1dHPjDqGGBE2Cnj2/NjomeQR25FkEAABmvhXArVXemJn3a69vJqL/SUTHy/4GxTCOGtLyCI5Y9HqsqRR8SSgTNAnWEGmhhqyYmUaI6CSKPDhEdGEkyxOzkmelwp5HUJIakjwCQYMwTppMZM8LNWSD39KxBIjoEwBeBOB4ItoF4N0AOgDAzB8EcAWAXyOiAcJs5dcys9A+BTH2EQzjHcoKUUO2qCExnQUNgFlYMS6zLu3bRG0TATNfmfP5BxCGlwomQBCkN68vFDVkqTUkm3YImgCTGpKFjhuikRWOVNRQ398ZtthJRw11AkIrp06RQLASYBZWlGAIN2QiWOEoW2sIsFBDElonaBDMwooSDOGGaGSFwxY1VDqhTCIqBA1CihrqSwkVF0QjKxyKxRmMGMxcPGrIyCOQTiJoCszCirGPQKxeE9LrVziICO0WYTgaoT9kMOdvSqNgqzUknUTQFIwtgr5QQ3kQjTQAQYswGLHW0Iv4CJK1hqSTCJqCtI9AqCEXRCMNQLtFGA65cHhcmFks1JCgmUhRQ5Iw6YT0+gYgtgiKrXgW2wF6UZleQDmLpZMImoF0HoFsvOSCaKQBaActDEeslZH2p4aApOksnUTQFOgVRwGhhrIgGmkAlEXQGxa1CMLz1Pck/V7QJAQtQicg9IaSUJYH6fUNgIoaGnOgBTKLgeSKSTqJoEnQQ6Rl4yU3RCMNQNpHUJQaGo7/SycRNAl69rzUGnJDNNIAhBYBF46TTvkICtQpEghWAvQQaaGG3JBe3wCMLYKC4XHphBuhhgTNgl5YURLK3BCNNADtVqt0HgEg1JCgudC3Y5VaQ27UphEi+ggRPUZE9zo+JyL6MyLaSUR3E9H5dcnSdKQzi4tTQ0XrFAkEKwEmNbTQbiHaGFGgoc5e/5cALsn4/FKEm9WfDuAqAH9RoyyNRjuIooYKO4vjhBtVp0hqDQmahIWEs3iIRdl0yYratMLMXwPwZMYplwP4GIf4JwDriGhDXfI0GbGPoKRF0B8KfypoJPR9uSVh0o1ZamUjgEe097uiYykQ0VVEtJ2Itu/Zs2cqwq0kxFFDxXwEq7SiXJJ1KWgiEtSQbLzkxIro9cx8LTNvY+Zt69evn7U4yw5mHoHvnsM6NSShdYImYrHTSpShloWOHbPUym4Am7X3m6JjgoJot1rjPIJ2i9D2ngjiqKExrSSms6BBMKkh37065g2z1MqNAF4XRQ9dBGAfMz86Q3lWLPQ8giIrHj2PQKghQRNhRg1JMIQd7bouTESfAPAiAMcT0S4A7wbQAQBm/iCAmwG8HMBOAIcAvLEuWZqOca2hgg190eojkI4iaA4SJSZk4yUnapsImPnKgHwfqQAAC+xJREFUnM8ZwFvquv88IWgRBkMuzIEqX0KCGpKOImgQFjtBInN+7arahrwVDen1DUCYR1A8IazVIiwEraRFID4CQYOgqKE4YVIsXhuk1zcAgXIWlwiPUyn4Qg0JmojFdgsjxjjzXhY6dohWGoC2VmKiaEMP9y2WhDJBM5EIkS4YTDFPEK00AEGrHDUExOF1ikeV8DpBkzAOiOgPhRrKgPT6BiC0CEalGrqKqhBqSNBE6IUVJaHMDdFKAxBoG9MUXdEvtFtSa0jQWJjZ8+IjsEO00gCUTSgDLBaBdBRBg6D6w1J/iJ5QQ05Ir28AghaNN6Yp5yMYxj4CKdMraBDUwuZgdxC+F4vXCtFKA5CIGirqI+i0xvxpkTpFAsFKgOoP+w/3o/fSvm0QrTQA4zyCEhyonkcgnUTQNKg2vX8pmgik1pAVkm/dAIyjhvpUnhoaDKWTCBqH2CIQaigLopUGIGgRRoxy1FC7hd5wFDnSpDkImgVlIR9YEmooC6KVBqDdCjfjHnHxhq427hBqSNBExNSQsgjE6rVBen4DEAQ0fl3cRxBo6ffSSQTNQspZLOHRVohWGgBlEQDFVzyqOqMU5BI0ESlnsVi9VohWGoCgFT/GsgllS1KQS9BAqMVN7CwWq9eGWns+EV1CRP9MRDuJ6O2Wz99ARHuIaEf09+Y65WkqEhZB4eqjAZiBp3sD6SSCxkElSIpFkI06t6oMAFwD4GcB7AJwOxHdyMz3G6dez8xvrUuOeUAwITUEhBzq+iMXK5VLIJg12kEL7RaNfQSrhP60ok6tXAhgJzP/CzP3AHwSwOU13m9ukfQRFKeGgDCqQnwEgiZisd2SqKEc1NnzNwJ4RHu/Kzpm4tVEdDcR3UBEm20XIqKriGg7EW3fs2dPHbKuaExmEcRRFdJJBE3EYieQEhM5mLVWvgBgKzOfA+AWANfZTmLma5l5GzNvW79+/VQFXAloTxI+Gp0/GLF0EkEjsdhuYTDi6LUsdmyos+fvBqCv8DdFx8Zg5ieYuRu9/RCAC2qUp7GYNGqo7HcFgpWARBsX+tOKOrVyO4DTiegUIloA8FoAN+onENEG7e1lAB6oUZ7GYrI8gvh8qTUkaCL0Ni5l1u2oLWqImQdE9FYAXwYQAPgIM99HRO8FsJ2ZbwTw60R0GYABgCcBvKEueZqMoAJncZnvCgQrAcoKWAhaaGl9RRCj1uqjzHwzgJuNY+/SXr8DwDvqlGEeMFkegUwEgmZDtWtp326IZhqAKqKGynxXIFgJUO1a/ANuiGYagHZVzmLpKIIGYqEdU0MCO0QzDcBkPgLdIpDmIGgextSQBEM4IT2/AVB5BEGJPYeTPgLpKILmQXwE+RDNNADKIijT0PXvLEhHETQQYx+BtG8nRDMNgIoaKjOQL0j4qKDhUFavWLxuSM9vACaxCHQHmnQUQRMR+whkuHNBNNMAqKihMgO5KtMLSEcRNBNCDeVDNNMATGIR6N+TjiJoIuL2LRavC9LzG4BJV/QqrE46iqCJiH0EMty5IJppAGKLoNxALhaBoMmQzOJ8iGYaAJVHMDE1JB1F0EAINZQP6fkNwOQ+AqGGBM2FUEP5EM00AJNEDQHSUQTNhkQN5UM00wAEkzqLxUcgaDCk1lA+pOc3AO0KqKEydYoEgpUAsQjyUatmiOgSIvpnItpJRG+3fL5IRNdHn99GRFvrlKepqCJqSDqJoKkQ6jMftWmGiAIA1wC4FMCZAK4kojON094E4ClmPg3A+wD8UV3yNBkTWwQdmQgEzYVEDeWjzt5/IYCdzPwvzNwD8EkAlxvnXA7guuj1DQBeQkSyqWhBBBMUnQPCDiKVRwVNhZoApI27UeeexRsBPKK93wXgx13nRJvd7wNwHIDH9ZOI6CoAVwHAli1b6pJ3xYKI8B9e8Ry88FnrS33/ygu34PnPPK5iqQSC5YFT1x+Bf/vTp5buH/OAWjevrwrMfC2AawFg27ZtPGNxliXe/FPPLP3dC085FheecmyF0ggEywftoIW3X3rGrMVY1qjTVtoNYLP2flN0zHoOEbUBHA3giRplEggEAoGBOieC2wGcTkSnENECgNcCuNE450YAr49eXwHgq8wsK36BQCCYImqjhiLO/60AvgwgAPARZr6PiN4LYDsz3wjgwwD+ioh2AngS4WQhEAgEgimiVh8BM98M4Gbj2Lu010sAfqFOGQQCgUCQDYmnEggEgjmHTAQCgUAw55CJQCAQCOYcMhEIBALBnINWWrQmEe0B8L2SXz8eRtbynGAef/c8/mZgPn/3PP5moPjvPpmZrenVK24imAREtJ2Zt81ajmljHn/3PP5mYD5/9zz+ZqDa3y3UkEAgEMw5ZCIQCASCOce8TQTXzlqAGWEef/c8/mZgPn/3PP5moMLfPVc+AoFAIBCkMW8WgUAgEAgMyEQgEAgEc465mQiI6BIi+mci2klEb5+1PHWAiDYT0a1EdD8R3UdEb4uOH0tEtxDRd6L/x8xa1jpARAER3UVEN0XvTyGi26Jnfn1UDr0xIKJ1RHQDET1IRA8Q0fPn4VkT0W9G7fteIvoEEa1q4rMmoo8Q0WNEdK92zPp8KcSfRb//biI6v8i95mIiIKIAwDUALgVwJoAriejM2UpVCwYAfpuZzwRwEYC3RL/z7QC+wsynA/hK9L6JeBuAB7T3fwTgfcx8GoCnALxpJlLVh/8B4EvMfAaAcxH+9kY/ayLaCODXAWxj5rMQlrh/LZr5rP8SwCXGMdfzvRTA6dHfVQD+osiN5mIiAHAhgJ3M/C/M3APwSQCXz1imysHMjzLzndHrAwgHho0If+t10WnXAfhXs5GwPhDRJgCvAPCh6D0BuBjADdEpjfrdRHQ0gBci3NMDzNxj5r2Yg2eNsHz+6mhXwzUAHkUDnzUzfw3hPi06XM/3cgAf4xD/BGAdEW3wvde8TAQbATyivd8VHWssiGgrgOcBuA3Aicz8aPTRDwGcOCOx6sT7AVwNYBS9Pw7AXmYeRO+b9sxPAbAHwEcjOuxDRHQEGv6smXk3gP8O4PsIJ4B9AO5As5+1DtfznWiMm5eJYK5AREcC+DSA32Dm/fpn0VagjYoZJqJXAniMme+YtSxTRBvA+QD+gpmfB+BpGDRQQ5/1MQhXv6cAeAaAI5CmT+YCVT7feZkIdgPYrL3fFB1rHIiog3AS+DgzfyY6/CNlJkb/H5uVfDXhBQAuI6KHEdJ+FyPkz9dF9AHQvGe+C8AuZr4ten8Dwomh6c/6ZwB8l5n3MHMfwGcQPv8mP2sdruc70Rg3LxPB7QBOjyILFhA6l26csUyVI+LFPwzgAWb+U+2jGwG8Pnr9egCfn7ZsdYKZ38HMm5h5K8Jn+1Vm/iUAtwK4IjqtUb+bmX8I4BEienZ06CUA7kfDnzVCSugiIloTtXf1uxv7rA24nu+NAF4XRQ9dBGCfRiHlg5nn4g/AywF8G8BDAH5v1vLU9Bt/EqGpeDeAHdHfyxHy5V8B8B0Afwvg2FnLWqMOXgTgpuj1MwF8E8BOAJ8CsDhr+Sr+recB2B49788BOGYenjWA9wB4EMC9AP4KwGITnzWATyD0g/QRWoBvcj1fAIQwMvIhAPcgjKryvpeUmBAIBII5x7xQQwKBQCBwQCYCgUAgmHPIRCAQCARzDpkIBAKBYM4hE4FAIBDMOdr5pwgEAgAgoiHC0Lw2gO8C+BUO6/sIBCsaYhEIBP44zMzncVj18kkAb5m1QAJBFZCJQCAoh39EVNSLiP6OiLZFr4+PSl2AiN5ARJ8hoi9F9eP/eHbiCgRuyEQgEBREtL/FS+BXpuQ8AK8BcDaA1xDR5pzzBYKpQyYCgcAfq4loB+Lyv7d4fOcrzLyPmZcQ1sQ5uU4BBYIykIlAIPDHYWY+D+FgToh9BAPEfWmV8Z2u9noICdAQLEPIRCAQFAQzH0K4XeJvR6WPHwZwQfTxFa7vCQTLFTIRCAQlwMx3Iaz6eSXCHbN+jYjuAnD8TAUTCEpAqo8KBALBnEMsAoFAIJhzyEQgEAgEcw6ZCAQCgWDOIROBQCAQzDlkIhAIBII5h0wEAoFAMOeQiUAgEAjmHP8flIFheAnaxOoAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "(0, 0): ───H───@─────────────────@───────────────────────────────────────────────X───Rz(-0.127π)───X───H───Rz(0.127π)───H───M('0')───\n",
            "               │                 │                                               │                 │\n",
            "(0, 1): ───H───X───Rz(-0.127π)───X───@─────────────────@─────────────────────────┼─────────────────┼───H───Rz(0.127π)───H───M('1')───\n",
            "                                     │                 │                         │                 │\n",
            "(1, 0): ───H─────────────────────────X───Rz(-0.127π)───X───@─────────────────@───┼─────────────────┼───H───Rz(0.127π)───H───M('2')───\n",
            "                                                           │                 │   │                 │\n",
            "(1, 1): ───H───────────────────────────────────────────────X───Rz(-0.127π)───X───@─────────────────@───H───Rz(0.127π)───H───M('3')───\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cthjxeUf6p81",
        "colab_type": "text"
      },
      "source": [
        "## Explanation of Code\n",
        "\n",
        "In what follows, we give a detailed description of the above code. \n",
        "###Define the qubits\n",
        "First, the number of qubits ($n=4$) is defined on a 2x2 grid and we instantiate the circuit object, which will contain the quantum program we wish to run on the qubits. \n",
        "### Prepare the Initial State\n",
        "Next, we prepare the initial state of the system, a uniform superposition over all basis states.  Thus, we append a Hadamard gate acting on each qubit to the circuit object.  As stated above, $p$ is set to 1 and $\\beta$ and $\\gamma$ are arbitrarily chosen in this implementation, however, in a real run of the algorithm, one would need to find the optimal values of these angles through brute force or classical pre-processing.  \n",
        "Next, recall that the goal is to create the state \n",
        "\n",
        "\\begin{equation} \\tag{10}\n",
        "|\\gamma, \\beta \\rangle = U(B,\\beta)U(C,\\gamma)|s \\rangle\n",
        "\\end{equation} \n",
        "\n",
        "Thus, we must define the unitary operators $U(C,\\gamma)$ and $U(B,\\beta)$ which will be appended to our circuit object, after the state initialization gates (Hadamard gates).  \n",
        "\n",
        "\n",
        "###Build the operator $U(C, \\gamma)$\n",
        "We begin by building up the operator $U(C, \\gamma)$, which is defined as:\n",
        "\n",
        "\\begin{equation} \\tag{11}\n",
        "U(C,\\gamma) = e^{-i{\\gamma}C} = \\prod_{ \\langle jk \\rangle} e^{-i{\\gamma}C_{<jk>}} = \\prod_{\\langle jk \\rangle} e^{-i\\frac{\\gamma}{2}(-\\sigma^z_j\\sigma^z_k +1)}\n",
        "\\end{equation} \n",
        "  \n",
        "\n",
        "Examaning the right-hand side of $(11)$, note that we can simplify this by dropping the identity term (the second term in the parantheses in the exponent), as this simple phase term will drop out once we make measurements of the qubits.  Intuitively, an identity operator should have no effect on the system.  Thus, we construct $U(C,\\gamma)$ as the following product of exponentials:\n",
        "  \n",
        "\\begin{equation} \\tag{11}\n",
        "U(C,\\gamma) = e^{-i\\frac{\\gamma}{2}(-\\sigma^z_1\\sigma^z_2)}e^{-i\\frac{\\gamma}{2}(-\\sigma^z_2\\sigma^z_3)}e^{-i\\frac{\\gamma}{2}(-\\sigma^z_3\\sigma^z_4)}e^{-i\\frac{\\gamma}{2}(-\\sigma^z_4\\sigma^z_1)}\n",
        "\\end{equation} \n",
        "  \n",
        "Each exponential acts on one pair of qubits, and can be translated into a quantum circuit using $Rz(\\theta)$ gates, which perform rotations of the spin about the *z*-axis through an angle of $\\theta$, and $CNOT$ gates which essentially entangle the two qubits in the pair.  \n",
        "\n",
        " As a specific example we examine how the first expoential operator in $(11)$ gets translated into quantum logic gates:\n",
        "  \n",
        "\\begin{eqnarray*} \\tag{12}\n",
        "    e^{-i\\frac{\\gamma}{2}(-\\sigma^z_1\\sigma^z_2)}  & \\rightarrow  &         CNOT[1,2]\\\\\n",
        "    &  & I[1] \\otimes Rz(2*-0.5*\\gamma)[2]\\\\\n",
        "    &  & CNOT[1,2]\n",
        "\\end{eqnarray*}\n",
        "\n",
        "\n",
        "  Here the right side indicates three gates are used to perform this operator: the $CNOT$ gate acts on qubits 1 and 2, then an $Rz(\\theta)$ gate is acted on qubit 2, and finally, another $CNOT$ gate is acted on qubits 1 and 2.  To show why this works, we simply need to show that the matrix representation of the left and right-hand sides of $(12)$ are the same.\n",
        "  \n",
        "We derive the matrix for the left-hand side first.  Since this operator acts on two qubits, it acts on a $2^2 = 4$ dimensional Hilbert space, and thus is represented by a 4x4 matrix.  The term in the exponential, $-i\\frac{\\gamma}{2}(-\\sigma^z_1\\sigma^z_2)$, is defined by the tensor product of the two Pauli-z terms multiplied by a coefficient:\n",
        "  \n",
        "\\begin{equation} \\tag{13}\n",
        "  -i\\frac{\\gamma}{2}(-\\sigma^z_1\\sigma^z_2) = i\\frac{\\gamma}{2}\\sigma^z_1 \\otimes \\sigma^z_2\n",
        "\\end{equation} \n",
        "  \n",
        "Now \n",
        "\\begin{equation} \\tag{14}\n",
        "  \\sigma^z_i = \\begin{bmatrix}\n",
        "    1 & 0\\\\\n",
        "    0 & -1\n",
        "\\end{bmatrix}\n",
        "\\end{equation} \n",
        "  \n",
        "So\n",
        " \n",
        "\\begin{equation} \\tag{15}\n",
        "  i\\frac{\\gamma}{2}\\sigma^z_1 \\otimes \\sigma^z_2= \n",
        "  i\\frac{\\gamma}{2}\\begin{bmatrix}\n",
        "    1 & 0 & 0 & 0\\\\\n",
        "    0 & -1 & 0 & 0 \\\\\n",
        "    0 & 0 & -1 & 0 \\\\\n",
        "    0 & 0 & 0 & 1\n",
        "\\end{bmatrix}\n",
        "\\end{equation} \n",
        "  \n",
        "And thus \n",
        " \n",
        "\\begin{equation} \\tag{16}\n",
        "  e^{i\\frac{\\gamma}{2}\\sigma^z_1 \\otimes \\sigma^z_2}= \n",
        "  \\begin{bmatrix}\n",
        "    e^{i\\frac{\\gamma}{2}} & 0 & 0 & 0\\\\\n",
        "    0 & e^{-i\\frac{\\gamma}{2}} & 0 & 0 \\\\\n",
        "    0 & 0 & e^{-i\\frac{\\gamma}{2}} & 0 \\\\\n",
        "    0 & 0 & 0 & e^{i\\frac{\\gamma}{2}}\n",
        "\\end{bmatrix}\n",
        "\\end{equation} \n",
        "  \n",
        "Now we derive the matrix representation of the right-hand side of (12).  First the $CNOT$ gate can be written as:\n",
        "\n",
        "\\begin{equation} \\tag{17}\n",
        "  CNOT= \n",
        "  \\begin{bmatrix}\n",
        "    1 & 0 & 0 & 0\\\\\n",
        "    0 & 1 & 0 & 0 \\\\\n",
        "    0 & 0 & 0 & 1 \\\\\n",
        "    0 & 0 & 1 & 0\n",
        "\\end{bmatrix}\n",
        "\\end{equation} \n",
        "\n",
        "Next, the $Rz(\\theta)$ term is defined as\n",
        "\\begin{equation} \\tag{18}\n",
        "  Rz(\\theta)= e^{-iZ\\frac{\\theta}{2}} = \n",
        "  \\begin{bmatrix}\n",
        "    e^{-i\\frac{\\theta}{2}} & 0 \\\\\n",
        "    0 & e^{i\\frac{\\theta}{2}} \n",
        "\\end{bmatrix}\n",
        "\\end{equation} \n",
        "\n",
        "Thus \n",
        "\n",
        "\\begin{eqnarray*}  \n",
        "  I \\otimes Rz(2*-0.5*\\gamma) & = & \n",
        "  \\begin{bmatrix}\n",
        "    1 & 0 \\\\\n",
        "    0 & 1 \n",
        "  \\end{bmatrix} \\otimes \n",
        "  \\begin{bmatrix}\n",
        "    e^{-i\\frac{\\gamma}{2}} & 0 \\\\\n",
        "    0 & e^{i\\frac{\\gamma}{2}} \n",
        "  \\end{bmatrix} \\\\\n",
        "  & = &  \\begin{bmatrix}  \\tag{19}\n",
        "    e^{i\\frac{\\gamma}{2}} & 0 & 0 & 0\\\\\n",
        "    0 & e^{-i\\frac{\\gamma}{2}} & 0 & 0 \\\\\n",
        "    0 & 0 & e^{i\\frac{\\gamma}{2}} & 0 \\\\\n",
        "    0 & 0 & 0 & e^{-i\\frac{\\gamma}{2}}\n",
        "\\end{bmatrix}\n",
        "\\end{eqnarray*}  \n",
        "\n",
        "Putting together the three gates we get:\n",
        "\n",
        "\n",
        "\\begin{equation} \\tag{20}\n",
        "  \\begin{bmatrix}\n",
        "    1 & 0 & 0 & 0\\\\\n",
        "    0 & 1 & 0 & 0 \\\\\n",
        "    0 & 0 & 0 & 1 \\\\\n",
        "    0 & 0 & 1 & 0\n",
        "\\end{bmatrix} * \\begin{bmatrix} \n",
        "    e^{i\\frac{\\gamma}{2}} & 0 & 0 & 0\\\\\n",
        "    0 & e^{-i\\frac{\\gamma}{2}} & 0 & 0 \\\\\n",
        "    0 & 0 & e^{i\\frac{\\gamma}{2}} & 0 \\\\\n",
        "    0 & 0 & 0 & e^{-i\\frac{\\gamma}{2}}\n",
        "\\end{bmatrix} *   \\begin{bmatrix}\n",
        "    1 & 0 & 0 & 0\\\\\n",
        "    0 & 1 & 0 & 0 \\\\\n",
        "    0 & 0 & 0 & 1 \\\\\n",
        "    0 & 0 & 1 & 0\n",
        "\\end{bmatrix} =   \\begin{bmatrix}\n",
        "    e^{i\\frac{\\gamma}{2}} & 0 & 0 & 0\\\\\n",
        "    0 & e^{-i\\frac{\\gamma}{2}} & 0 & 0 \\\\\n",
        "    0 & 0 & e^{-i\\frac{\\gamma}{2}} & 0 \\\\\n",
        "    0 & 0 & 0 & e^{i\\frac{\\gamma}{2}}\n",
        "\\end{bmatrix}\n",
        "\\end{equation} \n",
        "\n",
        "Notice the $(20)$ is identical to $(16)$, and thus we have proven that these three gates do indeed implement the first operator in $U(C,\\gamma)$.  The other operators are built analogously except that they act on different pairs of qubits.  Once the sub-circuit for $U(C,\\gamma)$ is defined, we append it to our main circuit.\n",
        "\n",
        "###Build the operator $U(B, \\beta)$\n",
        " \n",
        "In this example $U(B,\\beta)$ is given by \n",
        "\\begin{equation} \\tag{21}\n",
        "U(B,\\beta) = e^{-i{\\beta}\\sigma^x_1}e^{-i{\\beta}\\sigma^x_2} e^{-i{\\beta}\\sigma^x_3} e^{-i{\\beta}\\sigma^x_4}\n",
        "\\end{equation} \n",
        "\n",
        "Again we examine how to convert the first exponential operator into quantum logic gates:\n",
        "\\begin{eqnarray*} \\tag{22}\n",
        "    e^{-i{\\beta}\\sigma^x_1}  & \\rightarrow  &  H[1]\\\\\n",
        "    &  & Rz(2*\\beta)[1]\\\\\n",
        "    &  & H[1]\n",
        "\\end{eqnarray*}\n",
        "\n",
        "The derivation of this is much simpler.  Note that $\\sigma^x$ is diagonal in the x-basis, but not in the computational(z)-basis.  Since exponentiated operators are easy to carry out when the operator is diagonal, we apply a Hadamard gate on the qubit to rotate it into the x-basis, where this operator is now diagonal and represented by the $Rz(\\theta)$ gate.  We apply said $Rz(\\theta)$ gate to the qubit, and then apply a second Hadamard gate to the qubit to rotate it back into the computational basis.  Analogous gate sets are applied to all other qubits to carry out the full $U(B,\\beta)$ operator.  Once the sub-circuit for $U(B,\\beta)$ is defined, we append it to our main circuit.\n",
        "\n",
        "###Measurement and Simulation\n",
        "At this point, the main circuit now contains gates for initial state preparation and application of the $U(C,\\gamma)$ and $U(B,\\beta)$ unitary operators to get us into the final state \n",
        "\\begin{equation} \\tag{23}\n",
        "|\\gamma, \\beta \\rangle = U(B,\\beta)U(C,\\gamma)|s \\rangle\n",
        "\\end{equation} \n",
        "\n",
        "The next step of the algorithm is to measure each of the qubits to get the string $z$ and then evaluate $C(z)$.  Measurement is performed by appending a measurement operator on the computational basis to each of the qubits in our main circuit.  A simulation is carried out by instantiating a Simulator.  We then input the main circuit to this simulator, and since we will want to run this circuit many times, we can give an optional argument for the number of repetitions (in this case, 10).  \n",
        "\n",
        "The circuit will then be simulated 10 times.  The paper says that $m log(m)$ repetitions should suffice, and since in this case $m=4$, 10 repetitions are more than enough. The results of all runs are stored in the variable \"results\".  We can then evaluate the value of $C(z)$ for each of the runs and keep a running tab on which string $z$ gives the maximum value of $C(z)$, each of which is printed at the end of the program.  A diagram of the circuit is also output at the end of the program to give the reader a clearer understanding of the program that is being run on the quantum computer.\n",
        "\n",
        "To understand how this approximates the optimization of the MaxCut problem, note that $z = z_1z_2...z_n$ is a string, where each $z_i$ equals 0 or 1.  In the MaxCut problem, one wants to find a subset of the vertices $S$ such that the number of edges between $S$ and the complementary subset is maximal.  The final $z$ string we measure defines whether each vertex $i$ is in the subset $S$ (say, $z_i = 1$) or in the complement ($z_i = 0$).  $C(z)$ gives the number of edges that exist between the subset S and its complement.  So in our example, the 4-vertex ring, after enough repetitions, our QAOA finds the correct maximum cut of $C(z)=4$ and returns a string of alternating 0's and 1's, indicating the graph is maximally cut when alternating vertices are grouped into subsets.  This toy example was small and simple, which is why the QAOA was able to return the true optimal solution.  However, in more complex combinatorial optimization problems, this will not always be the case.  It may be necessary to increase the value of $p$, which in this simple case we took to just be 1.  \n",
        "  \n",
        "## MaxCut for Bounded Graph of Degree 2 with 16 Vertices and Brute Force Angle Optimization\n",
        "  \n",
        "In the previous example with 4 vertices, the algorithm almost always returned the optimal cut, despite our random selection of values for $\\beta$ and $\\gamma$.  Clearly, the problem was so small that the search space of possible solutions was easily navigated over the repeated runs.  However, if we move to a larger problem with 16 vertices, it becomes more important to find optimal values for $\\beta$ and $\\gamma$ in order to find the optimal cut with high probability.  \n",
        "  \n",
        "Below is some code that performs a grid search over values for the angles to find their optimal values.  Now, since $m=16$ it becomes necessary to increase the number of repetitions each circuit is run for to be $\\mathcal{O}(16log(16))$.  We, therefore, increase the number of repetitions to 100 in an attempt to keep it low enough for the code below not to take more than 5 minutes to run.  Upon completion, that program prints the resulting optimal values for $\\beta$, $\\gamma$, $C(z)$, and $z$.  It also plots a graph of how the value of $C(z)$ changes throughout the grid search as various values of $\\beta$ and $\\gamma$ are swept through.  It is clear from the plot that there is indeed an important angle-dependence now that our problem has more vertices, and thus resides in a larger search space.  \n",
        "  \n",
        "  \n",
        "**Note: Code below may take up to 5 minutes to run!**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m14wjd-WZWx8",
        "colab_type": "code",
        "outputId": "d1fcd849-557f-4416-b672-eeb2874ef102",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 962
        }
      },
      "source": [
        "#This code runs the QAOA, including optimization of the angles beta and gamma\n",
        "#for the example of MaxCut on a 2-regular graph with n=16 vertices and m=16 clauses\n",
        "#Brute force optimization of the angles beta ang gamma is performed by \n",
        "#a grid search over their possible values\n",
        "\n",
        "\n",
        "# define the length of grid.\n",
        "length = 4\n",
        "nqubits = length**2\n",
        "# define qubits on the grid.\n",
        "#in this case we have 16 qubits on a 4x4 grid\n",
        "qubits = [cirq.GridQubit(i, j) for i in range(length) for j in range(length)]\n",
        "\n",
        "#here, we use p=1\n",
        "#search for optimal angles beta and gamma by brute force\n",
        "#beta in [0,pi]\n",
        "#gamma in [0,2*pi]\n",
        "gridsteps = 19\n",
        "bstep = np.pi/gridsteps\n",
        "gstep = 2.0*np.pi/gridsteps\n",
        "overall_best_z = []*nqubits\n",
        "overall_best_Cz = 0.0\n",
        "all_Cz = []\n",
        "all_b = []\n",
        "all_g = []\n",
        "for b in range(0,gridsteps+1):\n",
        "  for g in range(0,gridsteps+1):\n",
        "    beta = bstep*b\n",
        "    gamma = gstep*g\n",
        "    all_b.append(b)\n",
        "    all_g.append(g)\n",
        "   \n",
        "   #instantiate a circuit\n",
        "    circuit = cirq.Circuit()\n",
        "    #apply Hadamard gate to all qubits to define the initial state\n",
        "    #here, the initial state is a uniform superposition over all basis states\n",
        "    circuit.append(cirq.H(q) for q in qubits)\n",
        "\n",
        "    #define operators for creating state |gamma,beta> = U_B*U_C*|s>\n",
        "    #define U_C operator = Product_<jk> { e^(-i*gamma*C_jk)} and append to main circuit\n",
        "    coeff = -0.5 #coefficient in front of sigma_z operators in the C_jk operator\n",
        "    U_C = cirq.Circuit()\n",
        "    for i in range(0,nqubits):\n",
        "      U_C.append(cirq.CNOT.on(qubits[i],qubits[(i+1)%nqubits]))\n",
        "      U_C.append(cirq.rz(2.0*coeff*gamma).on(qubits[(i+1)%nqubits]))\n",
        "      U_C.append(cirq.CNOT.on(qubits[i],qubits[(i+1)%nqubits]))\n",
        "    circuit.append(U_C)\n",
        "\n",
        "    #define U_B operator = Product_j {e^(-i*beta*X_j)} and append to main circuit\n",
        "    U_B = cirq.Circuit()\n",
        "    for i in range(0,nqubits):\n",
        "      U_B.append(cirq.H(qubits[i]))\n",
        "      U_B.append(cirq.rz(2.0*beta).on(qubits[i]))\n",
        "      U_B.append(cirq.H(qubits[i]))\n",
        "    circuit.append(U_B)\n",
        "\n",
        "    #add measurement operators for each qubit \n",
        "    #measure in the computational basis to get the string z\n",
        "    for i in range(0,nqubits):\n",
        "      circuit.append(cirq.measure(qubits[i],key=str(i)))\n",
        "\n",
        "    #run circuit in simulator to get the state |beta,gamma> and measure in the\n",
        "    #computational basis to get the string z and evaluate C(z)\n",
        "    #repeat for 100 runs and save the best z and C(z)\n",
        "    #simulator = cirq.google.XmonSimulator()\n",
        "    simulator = cirq.Simulator()\n",
        "    reps = 100\n",
        "    results = simulator.run(circuit, repetitions=reps)\n",
        "\n",
        "    #get bit string z from results\n",
        "    best_z = [None]*nqubits\n",
        "    best_Cz = 0.0\n",
        "    for i in range(0,reps):\n",
        "      z = []\n",
        "      for j in range (0,nqubits):\n",
        "        if (results.measurements[str(j)][i]):\n",
        "          z.append(1)\n",
        "        else:\n",
        "          z.append(-1)\n",
        "\n",
        "      #compute C(z)\n",
        "      Cz = 0.0\n",
        "      for j in range(0,nqubits):\n",
        "        Cz += 0.5*(-1.0*z[j]*z[(j+1)%nqubits] + 1.0)\n",
        "\n",
        "      #store best values for z and C(z)\n",
        "      if (Cz > best_Cz):\n",
        "        best_Cz = Cz\n",
        "        best_z = z\n",
        "    all_Cz.append(best_Cz)    \n",
        "    if (best_Cz > overall_best_Cz):\n",
        "      overall_best_Cz = best_Cz\n",
        "      overall_best_z = best_z\n",
        "      best_beta = beta\n",
        "      best_gamma = gamma\n",
        "        \n",
        "        \n",
        "    \n",
        "#print best string z and corresponding C(z)\n",
        "print(\"overall best z\")\n",
        "print(overall_best_z)\n",
        "print(\"overall best Cz\")\n",
        "print(overall_best_Cz)\n",
        "print(\"best beta\")\n",
        "print(best_beta)\n",
        "print(\"best gamma\")\n",
        "print(best_gamma)\n",
        "\n",
        "plt.plot(all_Cz)\n",
        "plt.xlabel(\"Iteration number in Grid Search\")\n",
        "plt.ylabel(\"Best C(z) value\")\n",
        "plt.show()\n",
        "\n",
        "#print a diagram of the circuit\n",
        "print(circuit)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "overall best z\n",
            "[-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]\n",
            "overall best Cz\n",
            "16.0\n",
            "best beta\n",
            "0.3306939635357677\n",
            "best gamma\n",
            "0.992081890607303\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "(0, 0): ───H───@────────────@─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────X───Rz(2π)───X───H───Rz(2π)───H───M('0')────\n",
            "               │            │                                                                                                                                                                                                                                                 │            │\n",
            "(0, 1): ───H───X───Rz(2π)───X───@────────────@────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼────────────┼───H───Rz(2π)───H───M('1')────\n",
            "                                │            │                                                                                                                                                                                                                                │            │\n",
            "(0, 2): ───H────────────────────X───Rz(2π)───X───@────────────@───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼────────────┼───H───Rz(2π)───H───M('2')────\n",
            "                                                 │            │                                                                                                                                                                                                               │            │\n",
            "(0, 3): ───H─────────────────────────────────────X───Rz(2π)───X───@────────────@──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼────────────┼───H───Rz(2π)───H───M('3')────\n",
            "                                                                  │            │                                                                                                                                                                                              │            │\n",
            "(1, 0): ───H──────────────────────────────────────────────────────X───Rz(2π)───X───@────────────@─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼────────────┼───H───Rz(2π)───H───M('4')────\n",
            "                                                                                   │            │                                                                                                                                                                             │            │\n",
            "(1, 1): ───H───────────────────────────────────────────────────────────────────────X───Rz(2π)───X───@────────────@────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼────────────┼───H───Rz(2π)───H───M('5')────\n",
            "                                                                                                    │            │                                                                                                                                                            │            │\n",
            "(1, 2): ───H────────────────────────────────────────────────────────────────────────────────────────X───Rz(2π)───X───@────────────@───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼────────────┼───H───Rz(2π)───H───M('6')────\n",
            "                                                                                                                     │            │                                                                                                                                           │            │\n",
            "(1, 3): ───H─────────────────────────────────────────────────────────────────────────────────────────────────────────X───Rz(2π)───X───@────────────@──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼────────────┼───H───Rz(2π)───H───M('7')────\n",
            "                                                                                                                                      │            │                                                                                                                          │            │\n",
            "(2, 0): ───H──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────X───Rz(2π)───X───@────────────@─────────────────────────────────────────────────────────────────────────────────────────────────────────┼────────────┼───H───Rz(2π)───H───M('8')────\n",
            "                                                                                                                                                       │            │                                                                                                         │            │\n",
            "(2, 1): ───H───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────X───Rz(2π)───X───@────────────@────────────────────────────────────────────────────────────────────────────────────────┼────────────┼───H───Rz(2π)───H───M('9')────\n",
            "                                                                                                                                                                        │            │                                                                                        │            │\n",
            "(2, 2): ───H────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────X───Rz(2π)───X───@────────────@───────────────────────────────────────────────────────────────────────┼────────────┼───H───Rz(2π)───H───M('10')───\n",
            "                                                                                                                                                                                         │            │                                                                       │            │\n",
            "(2, 3): ───H─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────X───Rz(2π)───X───@────────────@──────────────────────────────────────────────────────┼────────────┼───H───Rz(2π)───H───M('11')───\n",
            "                                                                                                                                                                                                          │            │                                                      │            │\n",
            "(3, 0): ───H──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────X───Rz(2π)───X───@────────────@─────────────────────────────────────┼────────────┼───H───Rz(2π)───H───M('12')───\n",
            "                                                                                                                                                                                                                           │            │                                     │            │\n",
            "(3, 1): ───H───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────X───Rz(2π)───X───@────────────@────────────────────┼────────────┼───H───Rz(2π)───H───M('13')───\n",
            "                                                                                                                                                                                                                                            │            │                    │            │\n",
            "(3, 2): ───H────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────X───Rz(2π)───X───@────────────@───┼────────────┼───H───Rz(2π)───H───M('14')───\n",
            "                                                                                                                                                                                                                                                             │            │   │            │\n",
            "(3, 3): ───H─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────X───Rz(2π)───X───@────────────@───H───Rz(2π)───H───M('15')───\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RjZ36ru9veKa",
        "colab_type": "code",
        "outputId": "0861129b-d141-4e2a-c520-f735f69c7c46",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        }
      },
      "source": [
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "from matplotlib import cm\n",
        "\n",
        "fig = plt.figure()\n",
        "ax = Axes3D(fig)\n",
        "surf = ax.plot_trisurf(all_b, all_g, all_Cz, cmap=cm.jet, linewidth=0.1)\n",
        "ax.set_xlabel('beta')\n",
        "ax.set_ylabel('gamma')\n",
        "ax.set_zlabel('best C(z) (out of 100 sims)')\n",
        "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
        "plt.show()"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jAtBEYb-ee38",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XN5tcnayyF_F",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}